Continuity with respect to the speed for optimal ship forms based on Michell's formula

Julien Dambrine (1) , Morgan Pierre (1)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]

We consider a ship hull design problem based on Michell's wave resistance. The half hull is represented by a nonnegative function and we seek the function whose support has a given area and which minimizes the total resistance for a given speed and a given displacement. We show that the optimal domain depends only on two parameters without dimension, the viscous drag coefficient and the Froude number of the area of the support. We prove that the optimal hull depends continuously on the Froude number and that the contribution of Michell's wave resistance vanishes as the Froude number tends to infinity. Numerical simulations confirm the theoretical results for large Froude numbers. For Froude numbers typically smaller than 1, the famous bulbous bow is numerically recovered. For intermediate Froude numbers, a "sinking" phenomenon occurs. It can be related to the nonexistence of a minimizer.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Julien Dambrine, Morgan Pierre. Continuity with respect to the speed for optimal ship forms based on Michell's formula. 2020. ⟨hal-02871885⟩